NE Sailboat kirjoitti:

What kind of glue, whatever will hold cut pieces of styrofoam coolers
together?

You could seal and glue the pieces together with ordinary
Sikaflex marine sealant with glue. After gluing you can
cover the inside surface by laminating glassfibre mat with
epoxy. Then apply some putty, and topcoat after that. If you
need to fasten the box inside a veneer box after that, then,
again Sikaflex. (And if your engine breaks apart, then
again, Sikaflex :-)).

TC